Abstract

Argument Systems provide a rich abstraction within which divers concepts of reasoning, acceptability and defeasibility of arguments, etc., may be studied using a unified framework. Two important concepts of the acceptability of an argument p in such systems are credulous acceptance to capture the notion that p can be `believed'; and sceptical acceptance capturing the idea that if anything is believed, then p must be. One important aspect affecting the computational complexity of these problems concerns whether the admissibility of an argument is defined with respect to `preferred' or `stable' semantics. One benefit of so-called `coherent' argument systems being that the preferred extensions coincide with stable extensions. In this note we consider complexity-theoretic issues regarding deciding if finitely presented argument systems modelled as directed graphs are coherent. Our main result shows that the related decision problem is (p) 2 --complete and is obtained solely via the graph-theoretic representation of an argument system, thus independent of the specific logic underpinning the reasoning theory.

Citations